We seek the posterior parameter distribution $p(\theta|D)$ where the parameter vector $\theta = [X_0,r,\alpha,\sigma]$, implementing primarily the Metropolis Hastings algorithm, and subsequently Adaptive Metropolis. Uniform priors are chosen for each of the target parameters: $$ p(X_0) = U(0,\infty), \quad p(r)=U(0,1), \quad p(\alpha)=U(0,\infty),\quad p(\sigma) = U(0,\infty). $$

Marginal Posteriors

Interpreting the posteriors...

Markov Chain Mixing

...(see Discussion).

Autocorrelation

ACF

Adaptive Metropolis Results

...